officially, today is washington's birthday - not his actual birthday (which falls on february 22) but rather the federal holiday to commemorate it. it's commonly referred to as president's day to honor "all presidents (even the lame and disgraced ones)" but most people associate this holiday with presidents washington and lincoln (two great ones) in particular.
for the record, it was the first federal holiday to honor an american citizen. congress tried, unsuccessfully, in 1968, to rename washington's birthday, "president's day" - and expand the focus to include all presidents. in the years since, a dozen states have renamed it.
personally, i'd stick with washington's birthday. don't dilute his legacy. if a other presidents are worthy enough for a day off, why not give each his own special day ;)